I'm interested in getting some opinions (or science) on a topic. Between the two exercises -- leg extensions and squats -- which one would recruit more muscle fibers in the quadriceps and place a greater tension load on those fibers?
I did a google search to resolve your question, but I didn't come up with any articles that tried to quantify differences in muscle fiber recruitment between the two movements.
However, the articles that I did see were overwhelming in their preference of the squat over the leg extension as an exercise. This is even true for rehabbing knee injuries - a sharp reversal of what I used to see 10 years or so ago. This
is a typical analysis:
Note that this research suggests that for individuals with anterior cruciate injuries, squats should be safer than isokinetic or isometric extension for quadriceps strengthening (leg extension), since forces acting on the ACL were lower during squatting, compared with both isokinetic and isometric extension. Yet, individuals with ACL injuries are often told to eschew squatting for extended periods of time - and instead work on leg-extension machines which actually may place more stress on the anterior cruciate ligament. For those with ACL problems, isokinetic flexion, isometric flexion, and squatting may safely be used for strengthening of the hamstrings, but note that isokinetic and isometric flexion are less 'functional' than squatting, i.e., they fail to duplicate the weight-bearing, synchronous multi-joint movements associated with sporting activity
And, for healthy individuals, squats lead to greater increases in usable strength than leg extensions.
Some bodybuilders use leg extensions to pre-exhaust their quads before squatting, and others use it as a finishing movement after squatting. But no bodybuilder has ever gotten contest-quality legs just by doing leg extensions.